Martin Kilian
Research Profile
Martin Kilian
Biography
As an undergraduate I studied Mathematics and Philosophy at TU Berlin, and wrote my Diploma thesis 'On the Riemann-Hilbert Problem' under the supervision of Ulrich Pinkall. I then moved to Amherst, Massachsuetts where I obtained a PhD in Mathematics in 2000 under the guidance of Franz Pedit. Then followed seven postdoctoral years with stops in Bennington, Amherst, Bath and Mannheim. I am a College Lecturer in Mathematics at UCC since 2007.
Research Interests
My research area is in Differential Geometry and Global Analysis. More specifically I work in surface theory, focusing on variational problems such as minimal surfaces, constant mean curvature surfaces and Willmore surfaces, see https://scholar.google.com/citations?user=uriH1FgAAAAJ&hl=en&oi=ao
Books
| Year | Publication | |
|---|---|---|
| (2021) | Minimal Surfaces: Integrable Systems and Visualisation.
m:iv Workshops, 201619 (2021) Minimal Surfaces: Integrable Systems and Visualisation. Switzerland: Springer. [ Publisher's Version] [DOI] [Details] |
Peer Reviewed Journals
| Year | Publication | |
|---|---|---|
| (2021) | 'On the elliptic sinhGordon equation with integrable boundary conditions'
Kilian, Martin; Smith, G. (2021) 'On the elliptic sinhGordon equation with integrable boundary conditions'. Nonlinearity, 34 (8):5119-5135 [DOI] [Full Text] [Details] |
|
| (2020) | 'Properly embedded minimal annuli in S2 x R'
L. Hauswirth, M. Kilian, M.U. Schmidt (2020) 'Properly embedded minimal annuli in S2 x R'. Journal of Integrable Systems, 5 (1):1-37 [ Publisher's Version] [DOI] [Details] |
|
| (2020) | 'Constant mean curvature trinoids with one irregular end'
M.Kilian, E.Mota, N.Schmitt (2020) 'Constant mean curvature trinoids with one irregular end'. Tohoku Mathematical Journal, 72 :317-333 [Details] |
|
| (2020) | 'On closed finite gap curves in spaceforms II'
S. Klein and M.Kilian (2020) 'On closed finite gap curves in spaceforms II'. Journal of Integrable Systems, 5 (1):1-25 [ Publisher's Version] [Details] |
|
| (2020) | 'On closed finite gap curves in spaceforms I'
S.Klein and M.Kilian (2020) 'On closed finite gap curves in spaceforms I'. Symmetry Integrability and Geometry-Methods and Applications, SIGMA 16 (2020), 011, 29 pages [ Publisher's Version] [Details] |
|
| (2016) | 'Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere'
L. Hauswirth, M. Kilian, M.U. Schmidt (2016) 'Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere'. Proceedings of the London Mathematical Society, 112 (3):588-622 [DOI] [Details] |
|
| (2015) | 'On mean-convex Alexandrov embedded surfaces in the 3-sphere'
L.Hauswirth, M.Kilian, M.U.Schmidt (2015) 'On mean-convex Alexandrov embedded surfaces in the 3-sphere'. Mathematische Zeitschrift, 281 (1):483-499 [DOI] [Details] |
|
| (2015) | 'Flows of constant mean curvature tori in the 3-sphere: The equivariant case'
M.Kilian, M.Schmidt, N.Schmitt (2015) 'Flows of constant mean curvature tori in the 3-sphere: The equivariant case'. Journal Fur Die Reine Und Angewandte Mathematik, 2015 (707):45-86 [ Publisher's Version] [DOI] [Details] |
|
| (2014) | 'On stability of equivariant minimal tori in the 3-sphere'
M.Kilian, M.U.Schmidt, N.Schmitt (2014) 'On stability of equivariant minimal tori in the 3-sphere'. Journal of Geometry and Physics, 85 :171-176 [ Publisher's Version] [DOI] [Details] |
|
| (2013) | 'Finite type minimal annuli in S2 x R'
L.Hauswirth, M. Kilian, M.Schmidt (2013) 'Finite type minimal annuli in S2 x R'. Illinois Journal of Mathematic, 57 (3):697-741 [Details] |
|
| (2013) | 'Constant mean curvature cylinders with irregular ends'
M.Kilian, N.Schmitt (2013) 'Constant mean curvature cylinders with irregular ends'. Journal of The Mathematical Society of Japan, 65 (3):775-786 [Details] |
|
| (2012) | 'Bubbletons are not embedded'
M Kilian; (2012) 'Bubbletons are not embedded'. Osaka Journal of Mathematics, 49 (3):653-663 [Details] |
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| (2010) | 'On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere'
M Kilian, M Schmidt; (2010) 'On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere'. OCAMI Studies, 3 :231-248 [ Publisher's Version] [Details] |
|
| (2008) | 'Delaunay ends of constant mean curvature surfaces'
M Kilian, W Rossman, N Schmitt; (2008) 'Delaunay ends of constant mean curvature surfaces'. Compositio Math, 144 :186-220 [Details] |
|
| (2007) | 'Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms'
N Schmitt, M Kilian, S Kobayashi, W Rossman ; (2007) 'Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms'. Journal of The London Mathematical Society, 75 :563-581 [Details] |
|
| (2006) | 'Equivariant harmonic cylinders'
F E Burstall, M Kilian ; (2006) 'Equivariant harmonic cylinders'. Quart. J. Math, 57 :449-468 [Details] |
|
| (2005) | 'Dressing preserving the fundamental group'
J Dorfmeister, M Kilian; (2005) 'Dressing preserving the fundamental group'. Differential Geom. Appl, 23 :176-204 [Details] |
|
| (2005) | 'Constant mean curvature surfaces of any positive genus'
M Kilian, S Kobayashi, W Rossman, N Schmitt; (2005) 'Constant mean curvature surfaces of any positive genus'. J. London Math. Soc, 72 :258-272 [Details] |
|
| (2004) | 'Dressing CMC n-Noids'
M Kilian, N Schmitt, I Sterling; (2004) 'Dressing CMC n-Noids'. Math. Z, 246 (3):501-519 [Details] |
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| (2004) | 'On the associated family of Delaunay surfaces'
M Kilian; (2004) 'On the associated family of Delaunay surfaces'. Proc. Amer. Math Soc, 132 (10):3075-3082 [Details] |
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| (2001) | 'Bäcklund transform of a perturbed Delaunay unduloid'
M Kilian, N Schmitt; (2001) 'Bäcklund transform of a perturbed Delaunay unduloid'. Electronic Geometry Models, [ Publisher's Version] [Details] |
|
| (2000) | 'New constant mean curvature surfaces'
M Kilian, I McIntosh, N Schmitt; (2000) 'New constant mean curvature surfaces'. Experiment. Math, 9 (4):595-611 [Details] |
Other Journals
| Year | Publication | |
|---|---|---|
| (2024) | 'On constant mean curvature surfaces satisfying integrable boundary conditions'
Martin Kilian (2024) 'On constant mean curvature surfaces satisfying integrable boundary conditions' Arxiv, . [ Publisher's Version] [Details] |
Conference Publications
| Year | Publication | |
|---|---|---|
| (2000) | 3rd European Congress of Mathematicians
M Kilian, N Schmitt; (2000) Surfaces, flows and holonomy . In: Sebastià Xambó-Descamps, Santiago Zarzuela eds. 3rd European Congress of Mathematicians [Details] |
Published Reports
| Year | Publication | |
|---|---|---|
| (2010) | Flows of equivariant constant mean curvature tori in the 3-sphere.
M Kilian; (2010) Flows of equivariant constant mean curvature tori in the 3-sphere. European Mathematical Society, Oberwolfach Report. [Details] |
|
| (2007) | Constant mean curvature surfaces with Delaunay ends.
M Kilian; (2007) Constant mean curvature surfaces with Delaunay ends. European Mathematical Society, Oberwolfach Report. [Details] |
Electronic Article
| Year | Publication | |
|---|---|---|
| (2023) | The space of genus two spectral curves of constant mean curvature tori in R3.
Emma Carberry, Martin Kilian, Sebastian Klein, Martin Ulrich Schmidt (2023) The space of genus two spectral curves of constant mean curvature tori in R3. Electronic Article [ Publisher's Version] [Details] |
Honours and Awards
| Year | Title | Awarding Body | |
|---|---|---|---|
| 2021 | Teaching Hero | T&L and USI | |
| 2003 | Postdoctoral Fellowship | EPSRC | |
| 2002 | Postdoctoral Fellowship | EDGE (European Commission FP 5) |
Professional Associations
| Association | Function | From / To | |
|---|---|---|---|
| Irish Mathematical Society | Member | 01-SEP-07 / |
Conference Contributions
| Year | Publication | |
|---|---|---|
| (2021) | Irish Geometry Seminar,
M.Kilian (2021) Integrable systems methods for constant mean curvature surfaces. [Invited Seminars/Guest Lectures], Irish Geometry Seminar, NUI Galway , 13-APR-21. [Details] |
|
| (2019) | Integrable Systems & Harmonic Maps 2019,
Martin Kilian (2019) On Finite Gap Curves. [Invited Lectures (Conference)], Integrable Systems & Harmonic Maps 2019, Technical University Vienna , 16-SEP-19 - 18-SEP-19. [Details] |
|
| (2019) | Minimal Surfaces, Integrable Systems and Visualization,
Martin Kilian (2019) Properly embedded minimal annuli in S2 x R. [Invited Lectures (Conference)], Minimal Surfaces, Integrable Systems and Visualization, University of Leicester , 02-SEP-19 - 06-SEP-19. [Details] |
|
| (2017) | Variational Methods in Submanifold Theory,
Martin Kilian (2017) Dressing curves. [Invited Lectures (Conference)], Variational Methods in Submanifold Theory, University of York , 30-MAY-17 - 02-JUN-17. [Details] |
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| (2017) | Irish Geometry Conference,
Martin Kilian (2017) On finite gap curves. [Invited Lectures (Conference)], Irish Geometry Conference, Maynooth University , 25-MAY-17 - 26-MAY-17. [Details] |
|
| (2015) | Workshop on Differential Geometry and Exterior Differential Systems,
M Kilian (2015) Finite type curves and beyond. [Invited Lectures (Conference)], Workshop on Differential Geometry and Exterior Differential Systems, University College Cork , 13-OCT-15 - 13-OCT-15. [Details] |
|
| (2014) | Workshop on Kähler Geometry and Geometric Analysis,
M Kilian (2014) Recent results in integrable surface geometry. [Invited Lectures (Conference)], Workshop on Kähler Geometry and Geometric Analysis, NUI Cork , 12-MAY-14 - 14-MAY-14. [Details] |
|
| (2014) | Irish Geometry Conference,
M Kilian (2014) On elastic Hopf-tori. [Invited Lectures (Conference)], Irish Geometry Conference, NUI Galway , 09-MAY-14 - 10-MAY-14. [Details] |
|
| (2013) | Variational Problems and Geometric PDE's,
M Kilian (2013) Elastic curves and Willmore Hopf-Tori. [Invited Lectures (Conference)], Variational Problems and Geometric PDE's, Granada University , 17-JUN-13 - 21-JUN-13. [Details] |
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| (2013) | Workshop on Advances in Surface Theory,
M Kilian (2013) On moduli spaces in integrable surface geometry. [Invited Lectures (Conference)], Workshop on Advances in Surface Theory, University of Leicester , 12-JUN-13 - 14-JUN-13. [Details] |
|
| (2012) | Navigating the space of surfaces,
Martin Kilian; (2012) Constrained Willmore tori of spectral genus one. [Invited Lectures (Conference)], Navigating the space of surfaces, Hausdorff Institute, Bonn , 26-MAR-12 - 30-MAR-12. [Details] |
|
| (2010) | Progress in Surface theory,
Martin Kilian; (2010) Flows of equivariant constant mean curvature tori in the 3-sphere. [Invited Lectures (Conference)], Progress in Surface theory, Oberwolfach , 02-MAY-10 - 08-MAY-10. [Details] |
|
| (2010) | Irish Geometry Conference,
Martin Kilian; (2010) Flows of equivariant cmc tori in the 3-sphere. [Invited Lectures (Conference)], Irish Geometry Conference, Maynooth , 14-MAY-10 - 15-MAY-10. [Details] |
|
| (2009) | British Mathematical Colloquium,
Martin Kilian; (2009) Flows of cmc surfaces. [Invited Lectures (Conference)], British Mathematical Colloquium, Galway , 06-APR-09 - 09-APR-09. [Details] |
|
| (2008) | Advances in surface theory,
Martin Kilian; (2008) The Lawson Conjecture. [Invited Lectures (Conference)], Advances in surface theory, Kloster Schoental , 05-MAR-08 - 05-MAR-08. [Details] |
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| (2008) | Uniqueness results in the theory of minimal surfaces,
Martin Kilian; (2008) Proof of the Lawson conjecture. [Invited Lectures (Workshops)], Uniqueness results in the theory of minimal surfaces, Université 7 Paris, France , 26-MAR-08 - 27-MAR-08. [Details] |
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| (2008) | Irish Mathematical Society, September Meeting 2008,
Martin Kilian; (2008) On the Lawson conjecture. [Invited Lectures (Conference)], Irish Mathematical Society, September Meeting 2008, CIT, Cork, , 01-SEP-08 - 02-SEP-08. [Details] |
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| (2008) | Advances in Surface Theory II,
Martin Kilian; (2008) Proof of the Lawson conjecture. [Invited Lectures (Conference)], Advances in Surface Theory II, Kloster Schöntal, Germany , 06-MAR-08 - 06-MAR-08. [Details] |
|
| (2008) | Geometry Day, Granada,
Martin Kilian; (2008) On CMC tori in the 3-sphere. [Invited Lectures (Conference)], Geometry Day, Granada, Universidad de Granada, Spain , 21-FEB-08 - 21-FEB-08. [Details] |
|
| (2008) | Riemann surfaces, harmonic maps and visualization; 16th Osaka City University International Academic Symposium 2008,
Martin Kilian (2008) On the Lawson conjecture. [Invited Lectures (Conference)], Riemann surfaces, harmonic maps and visualization; 16th Osaka City University International Academic Symposium 2008, Osaka City University, Japan , 15-DEC-09 - 20-DEC-09. [Details] |
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| (2007) | Progress in Surface theory,
Martin Kilian; (2007) CMC surfaces with Delaunay ends. [Invited Lectures (Conference)], Progress in Surface theory, Oberwolfach, Germany , 03-MAY-07 - 03-MAY-07. [Details] |
|
| (2006) | LMS Symposium,
Martin Kilian; (2006) On CMC tori in the 3-sphere. [Invited Lectures (Conference)], LMS Symposium, Durham University, UK , 20-AUG-06 - 20-AUG-06. [Details] |
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| (2005) | Advances in surface theory,
Martin Kilian; (2005) Equivariant harmonic maps. [Invited Lectures (Conference)], Advances in surface theory, Kloster Benediktbeuern, Germany , 27-JAN-05 - 27-JAN-05. [Details] |
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| (2004) | Variational Problems on surfaces,
Martin Kilian; (2004) CMC cylinders and Mathieu's equation. [Invited Lectures (Conference)], Variational Problems on surfaces, Granada, Spain , 06-FEB-04 - 06-FEB-04. [Details] |
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| (2003) | Differential Geometry of submanifolds and integrable systems,
Martin Kilian; (2003) Dressing and monodromy. [Invited Lectures (Conference)], Differential Geometry of submanifolds and integrable systems, Kobe, Japan , 12-JUL-03 - 12-JUL-03. [Details] |
|
| (2003) | EDGE Midterm meeting,
Martin Kilian; (2003) Dressing CMC n-noids. [Invited Lectures (Conference)], EDGE Midterm meeting, Pisa, Italy , 25-JAN-03 - 25-JAN-03. [Details] |
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| (2002) | Yorkshire Differential Geometry Day,
Martin Kilian; (2002) Constant mean curvature surfaces. [Invited Lectures (Conference)], Yorkshire Differential Geometry Day, Leeds, UK , 23-SEP-02 - 23-SEP-02. [Details] |
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| (2002) | Harmonic maps, minimal surfaces and geometric flows,
Martin Kilian; (2002) Constant mean curvature surfaces. [Invited Lectures (Conference)], Harmonic maps, minimal surfaces and geometric flows, Brest, France , 11-JUL-02 - 11-JUL-02. [Details] |
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| (2002) | EDGE Conference,
Martin Kilian; (2002) Dressing CMC surfaces. [Invited Lectures (Conference)], EDGE Conference, Edinburgh, UK , 02-AUG-02 - 02-AUG-02. [Details] |
|
| (2000) | Harmonic maps and curvature properties of submanifolds II,
Martin Kilian; (2000) Constant mean curvature cylinders. [Invited Lectures (Conference)], Harmonic maps and curvature properties of submanifolds II, Leeds, UK , 04-DEC-00 - 04-DEC-00. [Details] |
Committees
| Committee | Function | From / To | |
|---|---|---|---|
| Teaching, Learning and the Student Experience (TLSE), School of Mathematical Sciences | Chair | 2020 / | |
| Graduate Studies Committee, School of Mathematical Sciences | Chair | 2012 / 2016 | |
| Graduate Studies Committee SEFS | Member | 2012 / 2016 | |
| BComm Board of Studies | Member | 2009 / | |
| BComm Int Board of Studies | Member | 2009 / |
Employment
| Employer | Position | From / To | |
|---|---|---|---|
| University College Cork | College Lecturer in Mathematics | 01-AUG-07 / | |
| Universität Tübingen | Visiting Professor | 01-OCT-11 / 31-MAR-12 | |
| Universitaet Mannheim | Research Officer | 01-AUG-05 / 31-JUL-07 | |
| University of Bath | Research Officer | 01-FEB-02 / 31-JUL-05 | |
| Amherst College | Visiting Assistant Professor | 01-SEP-01 / 31-DEC-01 | |
| Bennington College | Visiting Assistant Professor | 01-SEP-00 / 31-AUG-01 |
Education
| Year | Institution | Qualification | Subject | |
|---|---|---|---|---|
| 2000 | University of Massachusetts, Amherst | PhD | Mathematics | |
| 1994 | TU Berlin | DIPLOMA | Mathematics, Philosophy |
Teaching Interests
- 2023 UCC: Topology, Multvariable Caclulus, Introduction to Analysis, Analysis II
- 2022 UCC: Topology, Multvariable Caclulus, Math for Engineers II
- 2021 UCC: Topology, Analysis I, Differential Geometry, Topics in Mathematics
- 2020 UCC: Multivariable Calculus, Math for Engineers II, Topology, Analysis I, Transformation Geometry
- 2019 UCC: Calculus, Transformation Geometry, Differential Geometry, Math for Engineers II
- 2018 UCC: Introduction to Analysis, Topics in Mathematics, Multivariable Calculus, Math for Engineers II
- 2017 UCC: Introduction to Analysis, Analysis I, Multivariable Calculus, Math for Engineers II
- 2016 UCC: Analysis I, Multivariable Calculus, Math for Engineers II
- 2015 UCC: Topology, Business Math I, Diff Geom I, Math for Engineers II
- 2014 UCC: Topology, Linear Algebra, Business Math I, Diff Geom II, Math for Engineers II;
- 2013 UCC: Topology, Linear Algebra, Business Math I, Diff Geom I;
- 2012 UCC: Topology, Linear Algebra, Business Math I, Diff Geom II;
- 2011 Tuebingen: Manifolds, Seminar on H-surfaces;
- 2010 UCC: Diff Geom I, Analysis I, Business Math I, Topology;
- 2009 UCC: Diff Geom I, Math for Engineers II, Business Math I, Transformation Geometry;
- 2008 UCC: Analysis I, Math for Engineers II, Topology, Transformation Geometry;
- 2007 UCC: Analysis I, Topology, Transformation Geometry;
- 2005 - 2006 Mannheim: Diff. equations, Surfaces I & II;
- 2002 - 2005 Bath: Analysis I, Diff. equations & control;
- 2001 Amherst College: Calculus I, Calculus III;
- 2000 Bennington College: Calculus I, II, III, Graph Theory, Course in C++;
- 1996 - 1999 UMASS: Calculus I, II, III; Linear Algebra I, II. Calculus for Social Sciences.
Recent Postgraduates
| Graduation Year | Student Name | Institution | Degree Type | Thesis Title | |
|---|---|---|---|---|---|
| 2019 | Eduardo Mota | University College Cork | PHD | Constant Mean Curvature surfaces and Heun's Differential Equations | |
| 2014 | Alan McCarthy | University College Cork | PhD | Flat surfaces of finite type in the 3-sphere |